Final Exam- Hypotheses Testing & T-Test

Question 1

Statistics

Answer 1

A branch of mathematics that involves the collection, analysis, and interpretation of data

Question 2

Descriptive Statistics

Answer 2

Procedures used to summarize a set of data

Question 3

Inferential Statistics

Answer 3

Are used to analyze data after you have conducted an experiment to determine whether your independent variable had a significant effect

Question 4

What is Significant?

Answer 4

An inferential statistical test can tell us whether the results of an experiment can occur frequency or rarely by chance.

• Inferential statistics with small values occur frequently by chance.
• Inferential statistics with large values occur rarely by chance.

Question 5

Null Hypothesis

Answer 5

A hypothesis that says that all difference between groups are due to chance. (i.e., not the operation of the IV)

• If a result occurs often by chance, we say that it is not significant and conclude that our IV did not affect the DV.
• If the result of our inferential statistical test occurs rarely by chance (i.e., it is significant), then we conclude that some factor other than chance is operative.

Question 6

Directional hypothesis

Answer 6

Specifies exactly how (i.e., the direction) the results will turn out.

Question 7

Nondirectional hypothesis

Answer 7

Does not specify exactly how the results will turn out.

Question 8

One-tail t test

Answer 8

Evaluates the probability of only one type of outcome (based on directional hypothesis)

Question 9

Two-tail t test

Answer 9

Evaluates the probability of both possible outcomes (based on nondirectional hypothesis)

Question 10

Basic Experiments

Answer 10

1. Define IV and DV
2. Set Null and Alternative Experimental Hypotheses
3. Take a random sample from population
   - The sample will represent your population (they have a characteristic in common)
4. The administration of the IV causes the samples to differ significantly
5. The experimenter generalizes the results of the experiment to the general population

Question 11

Overview of Six Steps of Experiment

Answer 11

1. Null Hypothesis
2. Alternative Hypothesis
3. Level of significance
4. Data collection and analysis
5. Criterion for evaluating data
6. Decision about rejecting/retaining null hypothesis

Question 12

Null Hypothesis (H0)

Answer 12

1. The assumption that there is no difference between groups
2. The hypothesis you are trying to disprove in your study
   - More generally, that phenomena in your theory are not operating as you predict

Question 13

Alternative Hypothesis (Ha or H1)

Answer 13

Deals with a specific value or specific difference

1. Typically this means testing to see if there are statistically significant differences between groups
2. Can be set up as directional or non-directional
   - Directional (one-tailed test): Males are expected to be smarter than females on math subsection
   - Non-directional (two-tailed test): Males and females will differ, but direction is not known
   - -Direction typically guided by theory
   - -Direction must be determined prior to data testing/analysis

Question 14

P-Value

Answer 14

A numerical measure of the statistical significance of a hypothesis test

• Tell us how likely it is that we could have gotten our sample data even if the null hypothesis is true
• Probability
• 0.05 or 0.01

Question 15

Type I Error

Answer 15

Rejecting the null when the null is actually true

• Evidence suggests that females are smarter than males (but this is correct)
• Accepting the experimental hypothesis when the null hypothesis is true.
• The experimenter directly controls the probability of making a Type I error by setting the significance level (i.e. p-value)
• The p-value is a measure of how likely you are to get this data if no real difference existed (i.e. if the null is true)
• You are less likely to make a Type-I error with a significance level of 0.01 than with a significance level of 0.05
• -However, the more extreme or critical you make the significance level to avoid a Type I error, the more likely you are to make a Type II (beta) error.

Question 16

Type II (beta) Error

Answer 16

Not rejecting the null when the null is actually false

• Evidence suggests that females and males are equally intelligent (but females are in fact smarter)
• A Type II error involves accepting the null hypothesis and rejecting a true experimental hypothesis
• -Type II errors are not under the direct control of the experimenter
• -We can indirectly cut down on Type II errors by implementing techniques that will cause our groups to differ as much as possible
• -For example, the use of a strong IV and larger groups of participants.

Question 17

Four potential outcomes

Answer 17

1. The null hypothesis is actually true and the test correctly fails to reject the null (there are no difference)
2. The null hypothesis is actually false, and the hypothesis test confirms the null is false (there are difference)
3. The null hypothesis is actually true, but the hypothesis test incorrectly rejects it (Type I error)
4. The null hypothesis is actually false, but the hypothesis test incorrectly fails to reject the null (Type II error)

Question 18

Lower alpha

Answer 18

Lower chance of Type I error

-Ex: 0.05 alpha means that the chances of rejecting a true null hypothesis equals 5 out of 100

Question 19

Calculated Value (Test statistic)

Answer 19

Summary of data leads to single numerical value (e.g., Pearson’s correlation r)

Question 20

P value

Answer 20

Indicates how likely it would be, assuming the null is true, to end up with a sample correlation as large or larger than the computed r.

Question 21

Critical Value

Answer 21

Value needed to be significant

• Set prior to data analyses
• Determined by alpha level (will be greater if alpha level is lower)
• Sample data statistics will be compared against the critical value
• Allows research to decide whether or not to reject the null

Question 22

Level of significance

Answer 22

Selecting a preset point on which the p-value must fall

• Standard in psychology is at the 0.05 level
• If p value is smaller than the criterion, the sample is viewed as inconsistent with null

Question 23

Failing to reject the null (or accepting the null)

Answer 23

Accepting the assumption that the null is true

• Intelligence scores for males and females were not significantly different
• Or…“No significant main effects were found”

Question 24

Rejecting the Null

Answer 24

Saying that the null is false

• Something is occurring
• Typically indicated by statistically significant differences (e.g. p<0.05)
• Ex: Females scored significantly higher than males

Question 25

Nonrandom Assignment to Groups

Answer 25

1. Random assignment tends to create equal groups in the long run
2. As groups get larger, we can place more confidence in random assignment achieving what we want it to
3. If we are faced with a situation in which we have fewer potential research participants and we are worried that random assignment may not create equal groups, what can we do?

Question 26

Correlated assignment

Answer 26

1. A method of assigning research participants to groups so that there is a relationship between small numbers of participant
2. These small groups are than randomly assigned to treatment conditions (matched assignment)

Question 27

Matched pairs

Answer 27

1. Research participants in a two-group design who are measured and equated on some variable before the experiment
   - Typically we measure a variable that could result in confounding if not controlled
   - After we have measured this variable, we create pairs of participants that are equal on this variable
   - After we have created our matched pairs, we then randomly assign participants from these pairs to the different treatment conditions

Question 28

Repeated measures

Answer 28

1. The same participants are tested in both treatment conditions of our experiment
2. The matched pairs are perfectly equal because they consist of the same people or animals tested across the entire experiment
3. No extraneous variables should be able to confound this situation because any difference between the participants’ performance in the two treatment conditions is due to the IV.
4. In this type of experiment, participants serve as their own controls.

Question 29

Natural pairs

Answer 29

1. Pairs of participants are created from naturally occurring pairs (e.g. biologically or socially related)

Question 30

Within-subjects comparison

Answer 30

1. Refers to a contrast between groups of participants who were assigned to groups through matched pairs, natural pairs, or repeated measures
   - We are essentially comparing scores within the same participants (subjects)
   - Although this direct comparison is literally true only for repeated-measures designs, participants in matched or natural pairs are the same with regard to the matching variable

Question 31

Choosing a two-group design

Answer 31

1. Random assignment should equate your groups adequately (assuming that you have large groups)
   - If you are using 20 or more participants per group, you can feel fairly safe that randomization will create equal groups.
   - If you are using 5 or fewer participants in a group, randomization may not work.

Question 32

Advantages of correlated groups designs

Answer 32

1. Control issues
   - The three methods for creating correlated-groups designs give us greater certainty of group equality.
2. Statistical issues
   - Correlated-groups designs can help reduce error variation

Question 33

Error variability

Answer 33

Variability in DV scores that is due to factors other than the IV_ individual differences, measurement error, and extraneous variation (within-groups variability)
*Statistic = Between-group variability/Error variability

Question 34

Advantages of independent-groups designs

Answer 34

1. Similarity

2. Use of correlated-groups designs is impossible in some situations

Question 35

True experiment

Answer 35

An experiment in which the experimenter directly manipulates the IV.

Question 36

Ex post facto research

Answer 36

A research approach in which the experimenter cannot directly manipulate the IV but can only classify, categorize, or measure the IV because it is predetermined in the participants (e.g. IV=sex)

Question 37

t Test

Answer 37

An inferential statistical test used to evaluate the difference between the means of two groups

Question 38

Degrees of freedom

Answer 38

The ability of a number in a specified set to assume any value

Question 39

Interpretation of t value

Answer 39

1. Determine the degrees of freedom (df) involved
2. Use the degrees of freedom to enter a t table
   - This table contains t values that occur by chance
   - Compare your t value to these chance values
   - To be significant, the calculated t must be equal to or larger than the one in the table.